[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-
- The sum of 3 consecutive even number is 144
- The lowest even number as 4x - 2
To Find :-
- We have to find the highest consecutive number.
Let's Begin :-
Here ,we have
- The sum of three consecutive even numbers is 144
- [ Consecutive even numbers are the sequence of numbers that differ by 2 or that are divisible by 2 ]
- The lowest even number is 4x - 2
Let the three consecutive number be
(4x - 2) , 4x , ( 4x + 2)
According to the question,
[tex]\sf{ (4x - 2) + 4x + ( 4x + 2) = 144}[/tex]
[tex]\sf{ 4x - 2 + 4x + 4x + 2 = 144}[/tex]
[tex]\sf{ 8x - 2 + 4x + 2 = 144}[/tex]
[tex]\sf{ 12x = 144}[/tex]
[tex]\sf{ x = }{\sf{\dfrac{ 144}{12}}}[/tex]
[tex]\sf{ x = }{\sf{\cancel{\dfrac{ 144}{12}}}}[/tex]
[tex]\sf{ x = 12 }[/tex]
Thus, The value of x is 12
Therefore,
The three consecutive even numbers are
- [tex]\sf{ 4x - 2 = 48 - 2 = 46 }[/tex]
- [tex]\sf{ 4x = 48 }[/tex]
- [tex]\sf{ 4x + 2 = 48 + 2 = 50 }[/tex]
Hence, The highest consecutive even number is 50 .
